Stationary in the COMSOL Multiphysics Programming Reference Manual
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For Automatic, Sj is the average of |Ui,j| for all DOFs i for fixed j, times a factor equal to 10−5 for highly nonlinear problems or 0.1 otherwise.
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For Manual, Sj is the value given in the Scale field. Sj is multiplied by a factor equal to 10−5 for highly nonlinear problems or 0.1 otherwise
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For Initial value based, Sj is the average of |Vi,j| for all DOFs i with fixed j times a factor equal to 10−5 for highly nonlinear problems or 0.1 otherwise. V = U0 is the solution vector corresponding to the initial value. In case all DOFs are zero for that particular field j, the total mean of |Vi,j| for all i and j is used instead.
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The (automatically damped Newton) nonlinear solver only checks the convergence criterion if the damping factor for the current iteration is equal to 1. The solver continues as long as the damping factor is not equal to 1 even if the estimated error is smaller than the requested relative tolerance.
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For Automatic, the weights are determined considering both the initial residual f0 and the residual after the first iteration f1 as . is the average of fi, j for all DOFs i for a fixed j. In case all fi, j are zero for that particular field j, the total mean of fi, j for all i and j is used instead.
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With consistent initialization active, the base residual f and the weights will be calculated during the consistent initialization and recalculated after the consistent initialization finishes.
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When the weights for field j need to be updated, then the weights are updated for all fields solved for in the fully coupled solver or in the same segregated step.
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For wave problems, the weights consist of two parts: the nonvelocity part and the velocity part . The weights are calculated using only the nonvelocity part of the residual f. The weights for the field j are defined to be proportional to the weights as . The proportional ratio r is a fieldwise quantity and is defined as , where F is the current residual. The weights are set to be 1 for the first iteration at the first time step. It is updated when the velocity part of the residual is nonzero for the first time. The velocity weights will be updated again when the nonvelocity weights are updated.
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Use the linear solver to solve a linearized (nonlinear) problem. See the section about linearity in Stationary Solver for details on how the residual is assembled in this case.
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The next factor is used to control the CFL number toward the requested target error estimate. A standard local error estimate control uses only a factor of this sort, but for this type of control, the absolute level of the error is not that important. However, without this factor (kI = 0), the CFL number might drift even though the error level is fluctuating on the same level. This factor can also be used to select an absolute regime for the error where increasing the CFL number should be more difficult.
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